SATHEE: Quantitative Aptitude Ques 1938

Quantitative Aptitude Ques 1938

Question: The angles of elevation of the top of a tower from two points which are at distances of 10 m and 5 m from the base of the tower and in the same straight line with it are complementary. The height of the tower is

Options:

A) $ 5m $

B) $ 15m $

C) $ \sqrt{50}m $

D) $ \sqrt{75}m $

Show Answer

Answer:

Correct Answer: C

Solution:

Given that, angles are complementary. Let h be the height of the tower. Now, in $ \Delta PBC, $ $ \tan \theta =\frac{h}{5} $ (i) and in $ \Delta PAC, $ $ \tan (90{}^\circ -\theta )=\frac{h}{10} $

$ \Rightarrow $ $ \cot \theta =\frac{h}{10} $ (ii) On multiplying Eqs. (i) and (ii), we get $ \tan \theta \cdot \cot \theta =\frac{h}{5}\times \frac{h}{10} $

$ \Rightarrow $ $ \frac{h^{2}}{50}=1 $
$ \Rightarrow $ $ h=\sqrt{50}m $ which is the required height of the tower.

Quantitative Aptitude Ques 1937

Quantitative Aptitude Ques 1939

Quantitative Aptitude Ques 1938

Question: The angles of elevation of the top of a tower from two points which are at distances of 10 m and 5 m from the base of the tower and in the same straight line with it are complementary. The height of the tower is

Options:

Answer:

Solution:

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